In this paper, the scaled group consensus problem of high-order multi-agent systems is investigated over directed graphs. In terms of an appropriate Lyapunov function, sufficient conditions are derived to guarantee scaled consensus for high-order continuous-time systems for strongly connected networks. For the case where the agents are subject to exogenous inputs, the scaled consensus is achieved with a guaranteed ${\mathcal{H}}_2$/${\mathcal{H}}_{\mathrm{\infty }}$ performance. Moreover, the scaled-consensus problem for multiagents subject Denial-of-Service (DoS) attack is investigated. The considered attack model allows the adversaries to compromise agents independently. Decay rates for each attack mode are obtained based on a set of linear matrix inequalities. Sufficient conditions in terms of decay rates are derived to guarantee secure scaled consensus. Simulation results are also presented to illustrate the effectiveness of the proposed theoretical results.

在本文中，在有向图上研究了高阶多智能体系统的缩放群共识问题。就适当的李雅普诺夫函数而言，推导出了充分条件以保证强连接网络的高阶连续时间系统的缩放共识。对于代理受外生输入影响的情况，缩放共识是通过有保证的${\mathcal{H}}_2$/${\mathcal{H}}_{\mathrm{\infty }}$表现。此外，还研究了多代理主体拒绝服务 (DoS) 攻击的缩放共识问题。所考虑的攻击模型允许对手独立地危害代理。基于一组线性矩阵不等式获得每种攻击模式的衰减率。推导出衰减率方面的充分条件以保证安全的规模化共识。还提供了仿真结果以说明所提出的理论结果的有效性。